Torque
Rotational force about a pivot.
Formula
Variables
Example
A 0.3 m wrench pushed with 50 N at 90° applies τ = 0.3·50 = 15 N·m.
How it works
Torque measures how strongly a force tends to turn an object around a pivot or axis. The formula τ = rF sinθ works because only the part of the force perpendicular to the lever arm produces rotation; the closer the push is to being parallel to the arm, the less turning effect it has. If the force is applied farther from the pivot, the turning effect increases because the same force acts with a larger moment arm.
When to use it
Use this formula whenever a force is applied to a door, wrench, beam, wheel, or any object that can rotate about a point. It is especially useful in mechanics, engineering design, statics, and problems involving levers or balancing moments.
Worked example, step by step
A mechanic applies a 120 N force to the end of a 0.40 m lever at an angle of 30° to the lever arm. τ = rF sinθ τ = (0.40)(120) sin(30°) τ = 48 × 0.5 τ = 24 N·m So the torque is 24 N·m.
Common mistakes to avoid
- Using the full force when the force is not perpendicular, instead of multiplying by sinθ
- Measuring r from the wrong point instead of from the pivot to where the force is applied
- Forgetting the angle must be between the force direction and the lever arm, not the floor or wall
Did You Know?
A longer wrench gives more torque for the same push — leverage in action.
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